A new computational approach to microwave heating of two-phase porous materials

Computational results for the microwave heating of a porous material are presented in this paper. Combined finite difference time domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent on both temperature and moisture content. The model was able to reflect the evolution of both temperature and moisture fields as well as energy penetration as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

Numerical simulation of free surface behaviour of a molten liquid metal droplet with and without electromagnetic induction

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to measure the physical properties of liquid metallic alloys such as surface tension or viscosity. Experiments can be conducted under terrestrial conditions or in microgravity, to reduce electromagnetic stirring and shaping of the droplet. Under such conditions, the time-dependent behaviour of a point of the free surface is recorded. Then the signal is analysed considering the droplet as a harmonic damped oscillator. We use a spectral code, for fluid flow and free surface descriptions, to check the validity of this assumption for two cases. First when the motion inside the droplet is generated by its initial distortion only and second, when the droplet is located in a uniform magnetic field originating far from the droplet. It is found that some deviations exist which can lead to an overestimate of the value of viscosity.

Droplet generation with modulated AC electromagnetic field at nozzle exit

A method of droplet generation based on applying a modulated AC high frequency magnetic field in the localized region of capillary breakup is considered as ans alternative to traditional methods for high temperature liquid melt droplet serial production by pressure variation. The method is based on a pseudo-spectral approximation with a coordinate transformation adaptin to the developing free surface. The electromagnetic field is recomputed continuously with the domain shape change. Practical application cases for liquid silicon droplets of 0.5 - 2 mm diameter are considered in detail.

Numerical modelling for electromagnetic processing of materials

Electromagnetic processing of materials (EPM) is one of the most widely practiced and fast growing applications of magnetic and electric forces to fluid flow. EPM is encountered in both industrial processes and laboratory investigations. Applications range in scale from nano-particle manipulation to tonnes of liquid metal treated in the presence of various configurations of magnetic fields. Some of these processes are specifically designed and made possible by the use of the electromagnetic force, like the magnetic levitation of liquid droplets, whilst others involve electric currents essential for electrothermal or electrochemical reasons, for instance, in electrolytic metal production and in induction melting. An insight for the range of established and novel EPM applications can be found in the review presented by Asai [1] in the EPM-2003 conference proceedings.

Droplet formation with electromagnetic pulse force

Methods for serial generation of droplets from a liquid jet are shortly reviewed. A method of liquid metal droplet generation based on AC high frequency magnetic field is considered in detail. Numerical model for direct simulation of the time dependent droplet generation process is presented. Computed examples demonstrate the liquid silicon droplet formation for the cases of 500-1500 μm diameter.

Time dependent electric, magnetic and hydrodynamic interaction in aluminium electrolysis cells

The waves in commercial cells for electrolytic aluminium production originate at the interface between the liquid aluminium and electrolyte, but their effect can spread into the surrounding busbar network as electric current perturbation, and the total magnetic field acquires a time dependent component. The presented model for the wave development accounts for the nonuniform electric current distribution at the cathode and the whole network of the surrounding busbars. The magnetic field is computed for the continuous current in the fluid zones, all busbars and the ferromagnetic construction elements. When the electric current and the associated magnetic field are computed according to the actual electrical circuit and updated for all times, the instability growth rate is significantly affected. The presented numerical model for the wave and electromagnetic interaction demonstrates how different physical coupling factors are affecting the wave development in the electrolysis cells. These small amplitude self-sustained interface oscillations are damped in the presence of intense turbulent viscosity created by the horizontal circulation velocity field. Additionally, the horizontal circulation vortices create a pressure gradient contributing to the deformation of the interface. Instructive examples for the 500 kA demonstration cell are presented.

A mathematical description of the acoustic coupling of the mass/spring model

This paper describes hybrid mathematical model which couples the mechanics of the mass/spring model to the acoustic wave propagation model for use in generating the acoustic signal emitted by complex structures of paper fibres under strain. A discussion of the coupling method is presented including remarks on the errors encountered intrinsic to the discretisation scheme. The numerical results of a vibrating rubber band and a vibrating paper fibre are compared to their experimental counterparts. The fundamental frequencies of the acoustic signals are compared showing a close agreement between the experimental and numerical results

Multiphysics simulation of microwave curing in micro-electronics packaging applications

Purpose – This paper aims to present an open-ended microwave curing system for microelectronics components and a numerical analysis framework for virtual testing and prototyping of the system, enabling design of physical prototypes to be optimized, expediting the development process. Design/methodology/approach – An open-ended microwave oven system able to enhance the cure process for thermosetting polymer materials utilised in microelectronics applications is presented. The system is designed to be mounted on a precision placement machine enabling curing of individual components on a circuit board. The design of the system allows the heating pattern and heating rate to be carefully controlled optimising cure rate and cure quality. A multi-physics analysis approach has been adopted to form a numerical model capable of capturing the complex coupling that exists between physical processes. Electromagnetic analysis has been performed using a Yee finite-difference time-domain scheme, while an unstructured finite volume method has been utilized to perform thermophysical analysis. The two solvers are coupled using a sampling-based cross-mapping algorithm. Findings – The numerical results obtained demonstrate that the numerical model is able to obtain solutions for distribution of temperature, rate of cure, degree of cure and thermally induced stresses within an idealised polymer load heated by the proposed microwave system. Research limitations/implications – The work is limited by the absence of experimentally derived material property data and comparative experimental results. However, the model demonstrates that the proposed microwave system would seem to be a feasible method of expediting the cure rate of polymer materials. Originality/value – The findings of this paper will help to provide an understanding of the behaviour of thermosetting polymer materials during microwave cure processing.

A modelling approach for coupling numerical analytical techniques applied in microsystems

In this paper, a method for the integration of several numerical analytical techniques that are used in microsystems design and failure analysis is presented. The analytical techniques are categorized into four groups in the discussion, namely the high-fidelity analytical tools, i.e. finite element (FE) method, the fast analytical tools referring to reduced order modeling (ROM); the optimization tools, and probability based analytical tools. The characteristics of these four tools are investigated. The interactions between the four tools are discussed and a methodology for the coupling of these four tools is offered. This methodology consists of three stages, namely reduced order modeling, deterministic optimization and probabilistic optimization. Using this methodology, a case study for optimization of a solder joint is conducted. It is shown that these analysis techniques have mutual relationship of interaction and complementation. Synthetic application of these techniques can fully utilize the advantages of these techniques and satisfy various design requirements. The case study shows that the coupling method of different tools provided by this paper is effective and efficient and it is highly relevant in the design and reliability analysis of microsystems

Numerical simulation of encapsulant curing within a variable frequency microwave processing system

Curing of encapsulant material in a simplified microelectronics package using an open oven Variable Frequency Microwave (VFM) system is numerically simulated using a coupled solver approach. A numerical framework capable of simulating electromagnetic field distribution within the oven system, plus heat transfer, cure rate, degree of cure and thermally induced stresses within the encapsulant material is presented. The discrete physical processes have been integrated into a fully coupled solution, enabling usefully accurate results to be generated. Numerical results showing the heating and curing of the encapsulant material have been obtained and are presented in this contribution. The requirement to capture inter-process coupling and the variation in dielectric and thermophysical material properties is discussed and illustrated with simulation results.

Models for magnetohydrodynamics of aluminium electrolysis cells

The electric current and the associated magnetic field in aluminium electrolysis cells create effects limiting the cell productivity and possibly cause instabilities: surface waving, ‘anode effects’, erosion of pot lining, feed material sedimentation, etc. The instructive analysis is presented via a step by step inclusion of different physical coupling factors affecting the magnetic field, electric current, velocity and wave development in the electrolysis cells. The full time dependent model couples the nonlinear turbulent fluid dynamics and the extended electromagnetic field in the cell, and the whole bus bar circuit with the ferromagnetic effects. Animated examples for the high amperage cells are presented. The theory and numerical model of the electrolysis cell is extended to the cases of variable cell bottom of aluminium layer and the variable thickness of the electrolyte due to the anode non-uniform burn-out process and the presence of the anode channels. The problem of the channel importance is well known Moreau-Evans model) for the stationary interface and the velocity field, and was validated against measurements in commercial cells, particularly with the recently published ‘benchmark’ test for the MHD models of aluminium cells [1]. The presence of electrolyte channels requires also to reconsider the previous magnetohydrodynamic instability theories and the dynamic wave development models. The results indicate the importance of a ‘sloshing’ parametrically excited MHD wave development in the aluminium production cells.

Effect of varying electromagnetic field on the VAR process

The three-dimensional, time-dependent electromagnetic field arising from the precession of the arc centre in a vacuum arc remelting furnace is shown (in a numerical simulation) to affect the fluid flow and heat transfer conditions near the solidification front in the upper part of the ingot.

Manufacturing of uniformly-sized silicon particles for solar cell from molten metal jet by electromagnetic pinch force

Spherical silicon solar cells are expected to serve as a technology to reduce silicon usage of photovoltaic (PV) power systems[1, 2, 3]. In order to establish the spherical silicon solar cell, a manufacturing method of uniformly sized silicon particles of 1mm in diameter is required. However, it is difficult to mass-produce the mono-sized silicon particles at low cost by existent processes now. We proposed a new method to generate liquid metal droplets uniformly by applying electromagnetic pinch force to a liquid metal jet[4]. The electromagnetic force was intermittently applied to the liquid metal jet issued from a nozzle in order to fluctuate the surface of the jet. As the fluctuation grew, the liquid jet was broken up into small droplets according to a frequency of the intermittent electromagnetic force. Firstly, a preliminary experiment was carried out. A single pulse current was applied instantaneously to a single turn coil around a molten gallium jet. It was confirmed that the jet could be split up by pinch force generated by the current. And then, electromagnetic pinch force was applied intermittently to the jet. It was found that the jet was broken up into mono-sized droplets in the case of a force frequency was equal to a critical frequency[5], which corresponds to a natural disturbance wave length of the jet. Numerical simulations of the droplet generation from the liquid jet were then carried out, which consisted of an electromagnetic analysis and a fluid flow calculation with a free surface of the jet. The simulation results were compared with the experiments and the agreement between the two was quite good.